Superconducting qubit dephasing times are limited by photon shot noise in the proximal readout resonator, due either to stray thermal photons or to coherent photons left over from measurement. At the same time, a small excess population of the qubit 1 state leads to error, and approaches to suppress this error based either on postselection or premeasurement and feedback are unsatisfactory. Here we describe the design and operation of tunable dissipative modes for the fast, deterministic initialization of linear cavities and qubits. We show that the dissipator can be used to provide a fast cavity reset following strong measurement and to suppress photon shot noise dephasing. Sideband gates applied to the qubit-cavity system followed by fast cavity reset are used to achieve high qubit initialization fidelity. We discuss prospects for the integration of tunable dissipators into a scalable multiqubit system.